What over-the-counter drug i can put on my swollen lips caused from a lip piercing?

Lip Swelling: Ice is considered as the best methods used for healing lip piercing. You can place an ice pack directly on the swollen area for some time and repeat this for a couple of times to get rid of the swelling. You can also suck on a fresh popsicle (made from mineral and pure water) to create the same effect as that of the ice pack.

Get it checked: If the swelling is caused by infection, you need to get treatment asap.